Question 1 (20 mins)

Use PyTorch to find the numerical solution to $2x^2-4x+1$

Question 2 (20 mins)

Implement a custom activation function $f(x) = ln(1 + e^x)$, and integrate it into a simple neural network to approximate a simple function.

Question 3 (10 mins)

Use ONNX/Netron tools to visualize resnet18 architecture from torchvision library

Question 4 (30 mins)

Design a neural network in PyTorch that has two parallel input branches, combines these inputs with additional data midway through the network, and then splits into two separate output branches.

1. Input Layer:
   • The network starts with two parallel input branches.
   • Each branch should accept an input tensor of shape (N, 10), where N is the batch size.
2. First and Second Branch:
   • Branch 1 and Branch 2 are identical in structure.
   • Each branch consists of the following layers:
     • A linear layer that expands the input from 10 to 20 features.
     • A ReLU activation layer.
     • Another linear layer that further expands from 20 to 30 features.
3. Midway Additional Inputs:
   • After the first and second branches, introduce an additional input tensor of shape (N, 5).
   • This additional input represents extra features to be combined with the outputs of the two branches.
4. Combination of Branch Outputs and Additional Input:
   • Concatenate the outputs of the two branches (each of shape (N, 30)) with the additional input (shape (N, 5)), resulting in a tensor of shape (N, 65).
5. Shared Layers After Combination:
   • Pass the combined tensor through a shared linear layer that reduces the dimension from 65 to 50.
   • Apply a ReLU activation function.
6. Two Separate Output Branches:
   • Split into two separate output branches after the shared layers.
   • Output Branch 1 and Output Branch 2:
     • Each output branch consists of a single linear layer that maps the 50 features to a single output feature (shape (N, 1)).